Question

Given the following prediction Sample ID Predicted Value Ground Truth 1 0.9 1 2 0.3 1 3 0.7 1 4 0.8 -1 5 0.4 -1 6 0.2 -1 (a) (18 Pts) Using 0.5 as the cutoff value, namely, the sample is predicted as 1 if predicted value >=0.5, otherwise -1. Please compute true positive rate (tpr, also called recall/sensitivity), false positive rate (fpr), true negative rate (tnr), false negative rate (fnr), accuracy and precision, respectively.

Answer 1

From what I understand, the data looks like this:

Sample ID	Predicted Value	Ground Truth
1	0.9	1
2	0.3	1
3	0.7	1
4	0.8	-1
5	0.4	-1
6	0.2	-1

Thus, the predicted values are 1, -1, 1, 1, -1, -1.

Thus, the confusion matrix will look as so:

	Predicted +1	Predicted -1
Actual +1	2	1
Actual -1	1	2

Thus,

true positive rate= tpr= 2/(2+1)

= 2/3= 0.67 or 67%

true negative rate= fpr= 2/(2+1)

= 2/3= 0.67 or 67%

false positive rate= 1- true negative rate

= 1-0.67= 0.33 or 33%

false negative rate= 1- true positive rate

= 1-0.67= 0.33 or 33%

accuracy= 4/6

= 2/3= 0.67 or 67%

precision= 2/3

= 0.67 or 67%